What is the directrix-2x^2-12x-23 ?

The directrix-2x^2-12x-23 is y=-39/8

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directrix-2x^2-12x-23

directrix

- 2 x^{2} - 12 x - 23

y = - \frac{39}{8}

Solution steps

Rewrite

y = - 2 x^{2} - 12 x - 23

in the standard form

4 (- \frac{1}{8}) (y - (- 5)) = (x - (- 3))^{2}

(h, k) = (- 3, - 5), p = - \frac{1}{8}

Parabola is symmetric around the y-axis and so the directrix is a line parallel to the x-axis, a distance

- p

from the center

(- 3, - 5)

y-coordinate

y = - 5 - p

y = - 5 - (- \frac{1}{8})

Refine

y = - \frac{39}{8}

2 x = (y - 3)^{2} + 4

y = \frac{x ^{2}}{28} - \frac{5 x}{14} + \frac{333}{28}

y = 3 x^{2} + x - 1

y = x^{2} - 5 x + 6

y = x^{2} - 5 x + 3